Top executives at medical device maker Medtronic Inc. said Monday they can save about $850 million over the next two to three years once the company closes on its $42.9 billion blockbuster deal to buy Mansfield-based Covidien PLC.

The cost-cutting moves — which will almost certainly include layoffs at Covidien — will help the Minneapolis company to invest about $10 billion in research and development in the United States over the coming decade, executives said in a conference call with investors and stock analysts.

Medtronic’s buyout of Covidien, unveiled late Sunday, is the largest in the history of the medical technology industry and the third-largest acquisition ever of a Massachusetts company. Covidien makes medical supplies and was formerly known as Tyco HealthCare. It has about 38,000 employees worldwide, including about 1,800 in Massachusetts.

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Medtronic agreed to pay $93.22 for each share of Covidien in a stock-and-cash deal that would create the world’s second-largest medical device company, after Johnson & Johnson. The price represents a 29 percent premium over Covidien’s closing stock price on Friday.

Shares of Covidien jumped 20.4 percent Monday to $86.75, a gain of $14.73 on the New York Stock Exchange.

Securities analysts said the mega-deal may foreshadow an acceleration of mergers and acquisitions in the medical technology sector as companies try to improve their bargaining clout with the hospitals and doctor practices to which they sell products and services.

“The Medtronic-Covidien merger will likely lead to additional consolidation in medtech as the companies try to gain negotiating power versus their increasingly larger and powerful customers,” Larry Biegelsen, a senior medical supplies and devices analyst for the New York financial firm Wells Fargo Securities, wrote in a note to investors.

Another medical device analyst, Tao Levy, managing director at the investment firm Wedbush Securities in New York, said that Medtronic and Covidien managers will spend a lot of time in the next few quarters working to integrate their organizations.

In the short term, he said, that could work to the advantage of their competitors, such as Natick-based Boston Scientific Corp.

“While we view the acquisition favorably for Covidien shareholders,” Levy wrote in an investor note, “we believe it leaves much to be desired on how Medtronic shareholders will benefit over the next couple of years.”

Echoing those misgivings, New York credit rating agency Standard & Poor’s placed a “credit watch” on its ratings for Medtronic, reflecting its expectation of a one- or two-notch downgrade if the buyout is completed as anticipated. “We estimate a substantial increase in Medtronic’s adjusted net leverage, based on the impact of cash used, incremental debt, and assumption of Covidien debt,” Standard & Poor’s analysts David A. Kaplan and Maryna Kandrukhin wrote in their credit report Monday.

Medtronic’s chief financial officer, Gary Ellis, told analysts that the cost savings from the Covidien acquisition will come initially from combining administrative and back-office operations and later from consolidating manufacturing plants and information technology systems around the globe.

“A lot of it is public company costs that have to be eliminated,” Ellis said. “We are committed to achieving that $850 million in synergy . . . We’re actually driving toward more than that.”

While promising to invest more aggressively in new products and innovation, especially in the United States, Medtronic executives downplayed the move of their headquarters to Ireland in an effort to reduce corporate tax liability. The company already has registered in Ireland as Medtronic PLC through a so-called tax inversion that allows it to take advantage of Covidien’s tax status there.

Covidien’s chief executive, Jose E. Almeida, told analysts the buyout will be “good for employees, good for our customers, and most important good for patients.”

He did not discuss the fate of Covidien’s corporate staff, though Ishrak said Medtronic hopes to retain many executives and managers from Covidien.

“This is one plus one equals five,” Almeida said. “This is a force multiplier that we could not have achieved by ourselves.”

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